Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 18 Aug 2011 12:39:43 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Aug/18/t1313685767l622wky6sv16bvx.htm/, Retrieved Wed, 15 May 2024 00:22:08 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=124118, Retrieved Wed, 15 May 2024 00:22:08 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsmattias debbaut
Estimated Impact97
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [tijdreeks A - Exp...] [2011-08-18 16:39:43] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
21571
21493
21422
21272
22747
22676
21571
20831
20909
20909
20980
21130
21051
21643
21864
21643
22455
21935
20759
20467
20467
20610
20026
20467
20097
20467
21051
21272
21792
21571
20246
19726
19506
19726
19363
19506
19064
19805
20168
20246
21643
21643
19805
19363
19363
19584
18622
18180
17668
17817
18480
17960
19363
19584
18180
17668
17375
17668
16855
16563
15388
15680
15751
15830
17226
17076
15388
14647
14355
14725
13322
12367
10601
10750
10750
10601
11854
11926
10451
10159
9568
10380
8905
8022
6333
6697
6255
6404
7509
7730
6996
6917
6917
7879
6184
5079
3163
4709
4488
4566
6333
6112
5300
5671
5671
6996
5450
4566
3163
5008
4859
4930
6476
6333
5813
5892
6255
7067
5813
4787




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=124118&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=124118&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=124118&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=124118&T=1

[TABLE]
[ROW][C]Estimated Parameters of Exponential Smoothing[/C][/ROW]
[ROW][C]Parameter[/C][C]Value[/C][/ROW]
[ROW][C]alpha[/C][C]1[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=124118&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=124118&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
321422214157
42127221344-72
522747211941553
622676226697
72157122598-1027
82083121493-662
92090920753156
10209092083178
112098020831149
122113020902228
132105121052-1
142164320973670
152186421565299
162164321786-143
172245521565890
182193522377-442
192075921857-1098
202046720681-214
21204672038978
222061020389221
232002620532-506
242046719948519
252009720389-292
262046720019448
272105120389662
282127220973299
292179221194598
302157121714-143
312024621493-1247
321972620168-442
331950619648-142
341972619428298
351936319648-285
361950619285221
371906419428-364
381980518986819
392016819727441
402024620090156
4121643201681475
42216432156578
431980521565-1760
441936319727-364
45193631928578
461958419285299
471862219506-884
481818018544-364
491766818102-434
501781717590227
511848017739741
521796018402-442
5319363178821481
541958419285299
551818019506-1326
561766818102-434
571737517590-215
581766817297371
591685517590-735
601656316777-214
611538816485-1097
621568015310370
631575115602149
641583015673157
6517226157521474
661707617148-72
671538816998-1610
681464715310-663
691435514569-214
701472514277448
711332214647-1325
721236713244-877
731060112289-1688
741075010523227
75107501067278
761060110672-71
7711854105231331
781192611776150
791045111848-1397
801015910373-214
81956810081-513
82103809490890
83890510302-1397
8480228827-805
8563337944-1611
8666976255442
8762556619-364
8864046177227
89750963261183
9077307431299
9169967652-656
9269176918-1
936917683978
94787968391040
9561847801-1617
9650796106-1027
9731635001-1838
98470930851624
9944884631-143
10045664410156
101633344881845
10261126255-143
10353006034-734
10456715222449
1055671559378
106699655931403
10754506918-1468
10845665372-806
10931634488-1325
110500830851923
11148594930-71
11249304781149
113647648521624
11463336398-65
11558136255-442
11658925735157
11762555814441
11870676177890
11958136989-1176
12047875735-948

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 21422 & 21415 & 7 \tabularnewline
4 & 21272 & 21344 & -72 \tabularnewline
5 & 22747 & 21194 & 1553 \tabularnewline
6 & 22676 & 22669 & 7 \tabularnewline
7 & 21571 & 22598 & -1027 \tabularnewline
8 & 20831 & 21493 & -662 \tabularnewline
9 & 20909 & 20753 & 156 \tabularnewline
10 & 20909 & 20831 & 78 \tabularnewline
11 & 20980 & 20831 & 149 \tabularnewline
12 & 21130 & 20902 & 228 \tabularnewline
13 & 21051 & 21052 & -1 \tabularnewline
14 & 21643 & 20973 & 670 \tabularnewline
15 & 21864 & 21565 & 299 \tabularnewline
16 & 21643 & 21786 & -143 \tabularnewline
17 & 22455 & 21565 & 890 \tabularnewline
18 & 21935 & 22377 & -442 \tabularnewline
19 & 20759 & 21857 & -1098 \tabularnewline
20 & 20467 & 20681 & -214 \tabularnewline
21 & 20467 & 20389 & 78 \tabularnewline
22 & 20610 & 20389 & 221 \tabularnewline
23 & 20026 & 20532 & -506 \tabularnewline
24 & 20467 & 19948 & 519 \tabularnewline
25 & 20097 & 20389 & -292 \tabularnewline
26 & 20467 & 20019 & 448 \tabularnewline
27 & 21051 & 20389 & 662 \tabularnewline
28 & 21272 & 20973 & 299 \tabularnewline
29 & 21792 & 21194 & 598 \tabularnewline
30 & 21571 & 21714 & -143 \tabularnewline
31 & 20246 & 21493 & -1247 \tabularnewline
32 & 19726 & 20168 & -442 \tabularnewline
33 & 19506 & 19648 & -142 \tabularnewline
34 & 19726 & 19428 & 298 \tabularnewline
35 & 19363 & 19648 & -285 \tabularnewline
36 & 19506 & 19285 & 221 \tabularnewline
37 & 19064 & 19428 & -364 \tabularnewline
38 & 19805 & 18986 & 819 \tabularnewline
39 & 20168 & 19727 & 441 \tabularnewline
40 & 20246 & 20090 & 156 \tabularnewline
41 & 21643 & 20168 & 1475 \tabularnewline
42 & 21643 & 21565 & 78 \tabularnewline
43 & 19805 & 21565 & -1760 \tabularnewline
44 & 19363 & 19727 & -364 \tabularnewline
45 & 19363 & 19285 & 78 \tabularnewline
46 & 19584 & 19285 & 299 \tabularnewline
47 & 18622 & 19506 & -884 \tabularnewline
48 & 18180 & 18544 & -364 \tabularnewline
49 & 17668 & 18102 & -434 \tabularnewline
50 & 17817 & 17590 & 227 \tabularnewline
51 & 18480 & 17739 & 741 \tabularnewline
52 & 17960 & 18402 & -442 \tabularnewline
53 & 19363 & 17882 & 1481 \tabularnewline
54 & 19584 & 19285 & 299 \tabularnewline
55 & 18180 & 19506 & -1326 \tabularnewline
56 & 17668 & 18102 & -434 \tabularnewline
57 & 17375 & 17590 & -215 \tabularnewline
58 & 17668 & 17297 & 371 \tabularnewline
59 & 16855 & 17590 & -735 \tabularnewline
60 & 16563 & 16777 & -214 \tabularnewline
61 & 15388 & 16485 & -1097 \tabularnewline
62 & 15680 & 15310 & 370 \tabularnewline
63 & 15751 & 15602 & 149 \tabularnewline
64 & 15830 & 15673 & 157 \tabularnewline
65 & 17226 & 15752 & 1474 \tabularnewline
66 & 17076 & 17148 & -72 \tabularnewline
67 & 15388 & 16998 & -1610 \tabularnewline
68 & 14647 & 15310 & -663 \tabularnewline
69 & 14355 & 14569 & -214 \tabularnewline
70 & 14725 & 14277 & 448 \tabularnewline
71 & 13322 & 14647 & -1325 \tabularnewline
72 & 12367 & 13244 & -877 \tabularnewline
73 & 10601 & 12289 & -1688 \tabularnewline
74 & 10750 & 10523 & 227 \tabularnewline
75 & 10750 & 10672 & 78 \tabularnewline
76 & 10601 & 10672 & -71 \tabularnewline
77 & 11854 & 10523 & 1331 \tabularnewline
78 & 11926 & 11776 & 150 \tabularnewline
79 & 10451 & 11848 & -1397 \tabularnewline
80 & 10159 & 10373 & -214 \tabularnewline
81 & 9568 & 10081 & -513 \tabularnewline
82 & 10380 & 9490 & 890 \tabularnewline
83 & 8905 & 10302 & -1397 \tabularnewline
84 & 8022 & 8827 & -805 \tabularnewline
85 & 6333 & 7944 & -1611 \tabularnewline
86 & 6697 & 6255 & 442 \tabularnewline
87 & 6255 & 6619 & -364 \tabularnewline
88 & 6404 & 6177 & 227 \tabularnewline
89 & 7509 & 6326 & 1183 \tabularnewline
90 & 7730 & 7431 & 299 \tabularnewline
91 & 6996 & 7652 & -656 \tabularnewline
92 & 6917 & 6918 & -1 \tabularnewline
93 & 6917 & 6839 & 78 \tabularnewline
94 & 7879 & 6839 & 1040 \tabularnewline
95 & 6184 & 7801 & -1617 \tabularnewline
96 & 5079 & 6106 & -1027 \tabularnewline
97 & 3163 & 5001 & -1838 \tabularnewline
98 & 4709 & 3085 & 1624 \tabularnewline
99 & 4488 & 4631 & -143 \tabularnewline
100 & 4566 & 4410 & 156 \tabularnewline
101 & 6333 & 4488 & 1845 \tabularnewline
102 & 6112 & 6255 & -143 \tabularnewline
103 & 5300 & 6034 & -734 \tabularnewline
104 & 5671 & 5222 & 449 \tabularnewline
105 & 5671 & 5593 & 78 \tabularnewline
106 & 6996 & 5593 & 1403 \tabularnewline
107 & 5450 & 6918 & -1468 \tabularnewline
108 & 4566 & 5372 & -806 \tabularnewline
109 & 3163 & 4488 & -1325 \tabularnewline
110 & 5008 & 3085 & 1923 \tabularnewline
111 & 4859 & 4930 & -71 \tabularnewline
112 & 4930 & 4781 & 149 \tabularnewline
113 & 6476 & 4852 & 1624 \tabularnewline
114 & 6333 & 6398 & -65 \tabularnewline
115 & 5813 & 6255 & -442 \tabularnewline
116 & 5892 & 5735 & 157 \tabularnewline
117 & 6255 & 5814 & 441 \tabularnewline
118 & 7067 & 6177 & 890 \tabularnewline
119 & 5813 & 6989 & -1176 \tabularnewline
120 & 4787 & 5735 & -948 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=124118&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]3[/C][C]21422[/C][C]21415[/C][C]7[/C][/ROW]
[ROW][C]4[/C][C]21272[/C][C]21344[/C][C]-72[/C][/ROW]
[ROW][C]5[/C][C]22747[/C][C]21194[/C][C]1553[/C][/ROW]
[ROW][C]6[/C][C]22676[/C][C]22669[/C][C]7[/C][/ROW]
[ROW][C]7[/C][C]21571[/C][C]22598[/C][C]-1027[/C][/ROW]
[ROW][C]8[/C][C]20831[/C][C]21493[/C][C]-662[/C][/ROW]
[ROW][C]9[/C][C]20909[/C][C]20753[/C][C]156[/C][/ROW]
[ROW][C]10[/C][C]20909[/C][C]20831[/C][C]78[/C][/ROW]
[ROW][C]11[/C][C]20980[/C][C]20831[/C][C]149[/C][/ROW]
[ROW][C]12[/C][C]21130[/C][C]20902[/C][C]228[/C][/ROW]
[ROW][C]13[/C][C]21051[/C][C]21052[/C][C]-1[/C][/ROW]
[ROW][C]14[/C][C]21643[/C][C]20973[/C][C]670[/C][/ROW]
[ROW][C]15[/C][C]21864[/C][C]21565[/C][C]299[/C][/ROW]
[ROW][C]16[/C][C]21643[/C][C]21786[/C][C]-143[/C][/ROW]
[ROW][C]17[/C][C]22455[/C][C]21565[/C][C]890[/C][/ROW]
[ROW][C]18[/C][C]21935[/C][C]22377[/C][C]-442[/C][/ROW]
[ROW][C]19[/C][C]20759[/C][C]21857[/C][C]-1098[/C][/ROW]
[ROW][C]20[/C][C]20467[/C][C]20681[/C][C]-214[/C][/ROW]
[ROW][C]21[/C][C]20467[/C][C]20389[/C][C]78[/C][/ROW]
[ROW][C]22[/C][C]20610[/C][C]20389[/C][C]221[/C][/ROW]
[ROW][C]23[/C][C]20026[/C][C]20532[/C][C]-506[/C][/ROW]
[ROW][C]24[/C][C]20467[/C][C]19948[/C][C]519[/C][/ROW]
[ROW][C]25[/C][C]20097[/C][C]20389[/C][C]-292[/C][/ROW]
[ROW][C]26[/C][C]20467[/C][C]20019[/C][C]448[/C][/ROW]
[ROW][C]27[/C][C]21051[/C][C]20389[/C][C]662[/C][/ROW]
[ROW][C]28[/C][C]21272[/C][C]20973[/C][C]299[/C][/ROW]
[ROW][C]29[/C][C]21792[/C][C]21194[/C][C]598[/C][/ROW]
[ROW][C]30[/C][C]21571[/C][C]21714[/C][C]-143[/C][/ROW]
[ROW][C]31[/C][C]20246[/C][C]21493[/C][C]-1247[/C][/ROW]
[ROW][C]32[/C][C]19726[/C][C]20168[/C][C]-442[/C][/ROW]
[ROW][C]33[/C][C]19506[/C][C]19648[/C][C]-142[/C][/ROW]
[ROW][C]34[/C][C]19726[/C][C]19428[/C][C]298[/C][/ROW]
[ROW][C]35[/C][C]19363[/C][C]19648[/C][C]-285[/C][/ROW]
[ROW][C]36[/C][C]19506[/C][C]19285[/C][C]221[/C][/ROW]
[ROW][C]37[/C][C]19064[/C][C]19428[/C][C]-364[/C][/ROW]
[ROW][C]38[/C][C]19805[/C][C]18986[/C][C]819[/C][/ROW]
[ROW][C]39[/C][C]20168[/C][C]19727[/C][C]441[/C][/ROW]
[ROW][C]40[/C][C]20246[/C][C]20090[/C][C]156[/C][/ROW]
[ROW][C]41[/C][C]21643[/C][C]20168[/C][C]1475[/C][/ROW]
[ROW][C]42[/C][C]21643[/C][C]21565[/C][C]78[/C][/ROW]
[ROW][C]43[/C][C]19805[/C][C]21565[/C][C]-1760[/C][/ROW]
[ROW][C]44[/C][C]19363[/C][C]19727[/C][C]-364[/C][/ROW]
[ROW][C]45[/C][C]19363[/C][C]19285[/C][C]78[/C][/ROW]
[ROW][C]46[/C][C]19584[/C][C]19285[/C][C]299[/C][/ROW]
[ROW][C]47[/C][C]18622[/C][C]19506[/C][C]-884[/C][/ROW]
[ROW][C]48[/C][C]18180[/C][C]18544[/C][C]-364[/C][/ROW]
[ROW][C]49[/C][C]17668[/C][C]18102[/C][C]-434[/C][/ROW]
[ROW][C]50[/C][C]17817[/C][C]17590[/C][C]227[/C][/ROW]
[ROW][C]51[/C][C]18480[/C][C]17739[/C][C]741[/C][/ROW]
[ROW][C]52[/C][C]17960[/C][C]18402[/C][C]-442[/C][/ROW]
[ROW][C]53[/C][C]19363[/C][C]17882[/C][C]1481[/C][/ROW]
[ROW][C]54[/C][C]19584[/C][C]19285[/C][C]299[/C][/ROW]
[ROW][C]55[/C][C]18180[/C][C]19506[/C][C]-1326[/C][/ROW]
[ROW][C]56[/C][C]17668[/C][C]18102[/C][C]-434[/C][/ROW]
[ROW][C]57[/C][C]17375[/C][C]17590[/C][C]-215[/C][/ROW]
[ROW][C]58[/C][C]17668[/C][C]17297[/C][C]371[/C][/ROW]
[ROW][C]59[/C][C]16855[/C][C]17590[/C][C]-735[/C][/ROW]
[ROW][C]60[/C][C]16563[/C][C]16777[/C][C]-214[/C][/ROW]
[ROW][C]61[/C][C]15388[/C][C]16485[/C][C]-1097[/C][/ROW]
[ROW][C]62[/C][C]15680[/C][C]15310[/C][C]370[/C][/ROW]
[ROW][C]63[/C][C]15751[/C][C]15602[/C][C]149[/C][/ROW]
[ROW][C]64[/C][C]15830[/C][C]15673[/C][C]157[/C][/ROW]
[ROW][C]65[/C][C]17226[/C][C]15752[/C][C]1474[/C][/ROW]
[ROW][C]66[/C][C]17076[/C][C]17148[/C][C]-72[/C][/ROW]
[ROW][C]67[/C][C]15388[/C][C]16998[/C][C]-1610[/C][/ROW]
[ROW][C]68[/C][C]14647[/C][C]15310[/C][C]-663[/C][/ROW]
[ROW][C]69[/C][C]14355[/C][C]14569[/C][C]-214[/C][/ROW]
[ROW][C]70[/C][C]14725[/C][C]14277[/C][C]448[/C][/ROW]
[ROW][C]71[/C][C]13322[/C][C]14647[/C][C]-1325[/C][/ROW]
[ROW][C]72[/C][C]12367[/C][C]13244[/C][C]-877[/C][/ROW]
[ROW][C]73[/C][C]10601[/C][C]12289[/C][C]-1688[/C][/ROW]
[ROW][C]74[/C][C]10750[/C][C]10523[/C][C]227[/C][/ROW]
[ROW][C]75[/C][C]10750[/C][C]10672[/C][C]78[/C][/ROW]
[ROW][C]76[/C][C]10601[/C][C]10672[/C][C]-71[/C][/ROW]
[ROW][C]77[/C][C]11854[/C][C]10523[/C][C]1331[/C][/ROW]
[ROW][C]78[/C][C]11926[/C][C]11776[/C][C]150[/C][/ROW]
[ROW][C]79[/C][C]10451[/C][C]11848[/C][C]-1397[/C][/ROW]
[ROW][C]80[/C][C]10159[/C][C]10373[/C][C]-214[/C][/ROW]
[ROW][C]81[/C][C]9568[/C][C]10081[/C][C]-513[/C][/ROW]
[ROW][C]82[/C][C]10380[/C][C]9490[/C][C]890[/C][/ROW]
[ROW][C]83[/C][C]8905[/C][C]10302[/C][C]-1397[/C][/ROW]
[ROW][C]84[/C][C]8022[/C][C]8827[/C][C]-805[/C][/ROW]
[ROW][C]85[/C][C]6333[/C][C]7944[/C][C]-1611[/C][/ROW]
[ROW][C]86[/C][C]6697[/C][C]6255[/C][C]442[/C][/ROW]
[ROW][C]87[/C][C]6255[/C][C]6619[/C][C]-364[/C][/ROW]
[ROW][C]88[/C][C]6404[/C][C]6177[/C][C]227[/C][/ROW]
[ROW][C]89[/C][C]7509[/C][C]6326[/C][C]1183[/C][/ROW]
[ROW][C]90[/C][C]7730[/C][C]7431[/C][C]299[/C][/ROW]
[ROW][C]91[/C][C]6996[/C][C]7652[/C][C]-656[/C][/ROW]
[ROW][C]92[/C][C]6917[/C][C]6918[/C][C]-1[/C][/ROW]
[ROW][C]93[/C][C]6917[/C][C]6839[/C][C]78[/C][/ROW]
[ROW][C]94[/C][C]7879[/C][C]6839[/C][C]1040[/C][/ROW]
[ROW][C]95[/C][C]6184[/C][C]7801[/C][C]-1617[/C][/ROW]
[ROW][C]96[/C][C]5079[/C][C]6106[/C][C]-1027[/C][/ROW]
[ROW][C]97[/C][C]3163[/C][C]5001[/C][C]-1838[/C][/ROW]
[ROW][C]98[/C][C]4709[/C][C]3085[/C][C]1624[/C][/ROW]
[ROW][C]99[/C][C]4488[/C][C]4631[/C][C]-143[/C][/ROW]
[ROW][C]100[/C][C]4566[/C][C]4410[/C][C]156[/C][/ROW]
[ROW][C]101[/C][C]6333[/C][C]4488[/C][C]1845[/C][/ROW]
[ROW][C]102[/C][C]6112[/C][C]6255[/C][C]-143[/C][/ROW]
[ROW][C]103[/C][C]5300[/C][C]6034[/C][C]-734[/C][/ROW]
[ROW][C]104[/C][C]5671[/C][C]5222[/C][C]449[/C][/ROW]
[ROW][C]105[/C][C]5671[/C][C]5593[/C][C]78[/C][/ROW]
[ROW][C]106[/C][C]6996[/C][C]5593[/C][C]1403[/C][/ROW]
[ROW][C]107[/C][C]5450[/C][C]6918[/C][C]-1468[/C][/ROW]
[ROW][C]108[/C][C]4566[/C][C]5372[/C][C]-806[/C][/ROW]
[ROW][C]109[/C][C]3163[/C][C]4488[/C][C]-1325[/C][/ROW]
[ROW][C]110[/C][C]5008[/C][C]3085[/C][C]1923[/C][/ROW]
[ROW][C]111[/C][C]4859[/C][C]4930[/C][C]-71[/C][/ROW]
[ROW][C]112[/C][C]4930[/C][C]4781[/C][C]149[/C][/ROW]
[ROW][C]113[/C][C]6476[/C][C]4852[/C][C]1624[/C][/ROW]
[ROW][C]114[/C][C]6333[/C][C]6398[/C][C]-65[/C][/ROW]
[ROW][C]115[/C][C]5813[/C][C]6255[/C][C]-442[/C][/ROW]
[ROW][C]116[/C][C]5892[/C][C]5735[/C][C]157[/C][/ROW]
[ROW][C]117[/C][C]6255[/C][C]5814[/C][C]441[/C][/ROW]
[ROW][C]118[/C][C]7067[/C][C]6177[/C][C]890[/C][/ROW]
[ROW][C]119[/C][C]5813[/C][C]6989[/C][C]-1176[/C][/ROW]
[ROW][C]120[/C][C]4787[/C][C]5735[/C][C]-948[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=124118&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=124118&T=2

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
321422214157
42127221344-72
522747211941553
622676226697
72157122598-1027
82083121493-662
92090920753156
10209092083178
112098020831149
122113020902228
132105121052-1
142164320973670
152186421565299
162164321786-143
172245521565890
182193522377-442
192075921857-1098
202046720681-214
21204672038978
222061020389221
232002620532-506
242046719948519
252009720389-292
262046720019448
272105120389662
282127220973299
292179221194598
302157121714-143
312024621493-1247
321972620168-442
331950619648-142
341972619428298
351936319648-285
361950619285221
371906419428-364
381980518986819
392016819727441
402024620090156
4121643201681475
42216432156578
431980521565-1760
441936319727-364
45193631928578
461958419285299
471862219506-884
481818018544-364
491766818102-434
501781717590227
511848017739741
521796018402-442
5319363178821481
541958419285299
551818019506-1326
561766818102-434
571737517590-215
581766817297371
591685517590-735
601656316777-214
611538816485-1097
621568015310370
631575115602149
641583015673157
6517226157521474
661707617148-72
671538816998-1610
681464715310-663
691435514569-214
701472514277448
711332214647-1325
721236713244-877
731060112289-1688
741075010523227
75107501067278
761060110672-71
7711854105231331
781192611776150
791045111848-1397
801015910373-214
81956810081-513
82103809490890
83890510302-1397
8480228827-805
8563337944-1611
8666976255442
8762556619-364
8864046177227
89750963261183
9077307431299
9169967652-656
9269176918-1
936917683978
94787968391040
9561847801-1617
9650796106-1027
9731635001-1838
98470930851624
9944884631-143
10045664410156
101633344881845
10261126255-143
10353006034-734
10456715222449
1055671559378
106699655931403
10754506918-1468
10845665372-806
10931634488-1325
110500830851923
11148594930-71
11249304781149
113647648521624
11463336398-65
11558136255-442
11658925735157
11762555814441
11870676177890
11958136989-1176
12047875735-948







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
12147093093.218617846476324.78138215353
12246312345.940055528546916.05994447146
12345531754.384552186237351.61544781377
12444751243.437235692957706.56276430705
1254397784.0029927261518009.99700727385
1264319361.1600778349128276.83992216509
1274241-33.95571022644628515.95571022645
1284163-407.1198889429228733.11988894292
1294085-762.3441464605788932.34414646058
1304007-1102.549368500089116.54936850008
1313929-1429.94058784519287.9405878451
1323851-1746.230895627549448.23089562754

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 4709 & 3093.21861784647 & 6324.78138215353 \tabularnewline
122 & 4631 & 2345.94005552854 & 6916.05994447146 \tabularnewline
123 & 4553 & 1754.38455218623 & 7351.61544781377 \tabularnewline
124 & 4475 & 1243.43723569295 & 7706.56276430705 \tabularnewline
125 & 4397 & 784.002992726151 & 8009.99700727385 \tabularnewline
126 & 4319 & 361.160077834912 & 8276.83992216509 \tabularnewline
127 & 4241 & -33.9557102264462 & 8515.95571022645 \tabularnewline
128 & 4163 & -407.119888942922 & 8733.11988894292 \tabularnewline
129 & 4085 & -762.344146460578 & 8932.34414646058 \tabularnewline
130 & 4007 & -1102.54936850008 & 9116.54936850008 \tabularnewline
131 & 3929 & -1429.9405878451 & 9287.9405878451 \tabularnewline
132 & 3851 & -1746.23089562754 & 9448.23089562754 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=124118&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]121[/C][C]4709[/C][C]3093.21861784647[/C][C]6324.78138215353[/C][/ROW]
[ROW][C]122[/C][C]4631[/C][C]2345.94005552854[/C][C]6916.05994447146[/C][/ROW]
[ROW][C]123[/C][C]4553[/C][C]1754.38455218623[/C][C]7351.61544781377[/C][/ROW]
[ROW][C]124[/C][C]4475[/C][C]1243.43723569295[/C][C]7706.56276430705[/C][/ROW]
[ROW][C]125[/C][C]4397[/C][C]784.002992726151[/C][C]8009.99700727385[/C][/ROW]
[ROW][C]126[/C][C]4319[/C][C]361.160077834912[/C][C]8276.83992216509[/C][/ROW]
[ROW][C]127[/C][C]4241[/C][C]-33.9557102264462[/C][C]8515.95571022645[/C][/ROW]
[ROW][C]128[/C][C]4163[/C][C]-407.119888942922[/C][C]8733.11988894292[/C][/ROW]
[ROW][C]129[/C][C]4085[/C][C]-762.344146460578[/C][C]8932.34414646058[/C][/ROW]
[ROW][C]130[/C][C]4007[/C][C]-1102.54936850008[/C][C]9116.54936850008[/C][/ROW]
[ROW][C]131[/C][C]3929[/C][C]-1429.9405878451[/C][C]9287.9405878451[/C][/ROW]
[ROW][C]132[/C][C]3851[/C][C]-1746.23089562754[/C][C]9448.23089562754[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=124118&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=124118&T=3

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
12147093093.218617846476324.78138215353
12246312345.940055528546916.05994447146
12345531754.384552186237351.61544781377
12444751243.437235692957706.56276430705
1254397784.0029927261518009.99700727385
1264319361.1600778349128276.83992216509
1274241-33.95571022644628515.95571022645
1284163-407.1198889429228733.11988894292
1294085-762.3441464605788932.34414646058
1304007-1102.549368500089116.54936850008
1313929-1429.94058784519287.9405878451
1323851-1746.230895627549448.23089562754



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Double ; par3 = additive ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')